The diffusion variables provide a physical method for organizing the genomic information that continues to emerge, in a way that reveals both larger scale geometries and finer details compared to alternative embedding methods [1]}, [2]} (Supplementary Information; Figs. S1-S4). From the perspective of microbial systems, diffusion distances in trait space (e.g., Fig. 3A) provide a powerful proxy for ecological similarities that can complement insights from current phylogenetic methods [3]}, [4]}. Traits used to calculate diffusion distances need not be derived from metabolic reconstructions of whole genomes as in the present analysis, but could comprise functional information identified, for instance, through species-level profiling [5]} of metagenomic or metatranscriptomic shotgun sequencing data. From an ecological point of view the present analysis constitutes the most extensive mapping of a niche space geometry so far, and facilitates the application of ecological theories to data describing bacterial communities.
